Phase diagrams of ternary mixtures at constant pressure

Ternary systems are made of three constituents. Let us denote the three constituents by A, B, and C. The mole fractions of the constituents are related to one another:

∑

where x_i denotes the mole fraction of the constituents A, B or C. The diagrams, as pre-sented in Fig.(2.4) are three-dimensional but for ease of drawing and interpretation it is convenient to handle them by considering the isotherm in two dimensions. Along the

Figure 2.4: Ternary phase diagram at constant pressure.

line connecting two constituents the mole fraction of the third one must be zero. At any vortex, the mole fraction of one constituent is 1.0 while that of both others zero. An exam-ple of such isothermal diagram is shown in Fig(2.5). Obviously, the thermodynamics of ternary mixtures is more complicated as that of binary mixtures. The stability criterions discussed in Section (2.1) have to be extended to include the third component. Details of calculations and the underlying theory are given in the paper by Sadus [44]. Here only a brief outline about the conditions and criterions of the existence of a critical point in a ternary liquid system is presented. The third constituent makes it necessary to extend the before mentioned criterion of stability by an additional quantity, the diffusion coefficient D₀:

Figure 2.5: Example of an isotherm for a phase diagram of a ternary mixture: The mixing point, represented by the dot, is composed of the components A with x_A=0.4, B with x_B=0.35 and C with x_C=0.25.,∑x_i=1.

while F=U−T S and the condition for the third constituent follows from Eq.(2.19) and is x_C=1−x_A−x_B. However, due to the reduction of the stability area and the equilibrium area to only one line, the following relation has to be fulfilled at the critical point:

P_c0= Porter-attempt [40] into account, it is possible to assess the shape and the position of the critical line. A considerable diversity of critical equilibria can potentially be ob-served in a ternary mixture. Fig.(2.6) shows the existing types of phase diagrams, based on phenomenological interpretation of models of critical systems. In this thesis type 2a diagrams are important and are thus considered in more detail. Diagrams of type 2a re-sult from mixing of two binary upper-critical-point mixtures with a common component.

Figure 2.6: Phase diagrams for ternary liquids at constant pressure. The dashed lines show equilibrium tie lines and the full lines binodales.

Figure 2.7: An hypothetical phase diagram of Type 2a of the ternary system ABC:a) Points (•) refer to the line of plait points. Different isothermal binodal curves are represented at temperatures T₁, ...,T₂. b) The plait point line as a function mole fraction of A, from the binary system CB to AB.

The mixing behavior of ternary systems of type 2a is illustrated in Fig.(2.7). This kind of particular class of ternary liquid systems has been first found by Francis [45] in 1953.

However, at constant pressure one can follow the line of so-called plait points between the demixing points of two limiting binary liquid systems. In the the case of Fig.(2.7(a)) it is the binary system CB and the binary system AB. Each of these plait points represents the critical consolute point of a critical composition of the ternary system A, B and C.

At these points criterions for critical behavior like the equal-volume criterion or critical opalescence are fulfilled. In certain temperature ranges, the hypothetical systems under consideration, have two separate binodal lines. On lowering the temperature the two lines coincide at both plait points. Consequently, a new significant point appears, the so-called col point or saddle point. This behavior emerges when two conditions are satisfied. First, in the range of temperatures considered two components are miscible and the third one is partially miscible with both others up to the respective binary critical solution temper-atures, as shown in Fig.(2.7(b)). Second, the critical consolute point must be quite close the critical point of the other binary system. In conclusion, in the triangular tempera-ture/composition prism of the ternary system, the binodal surface is concave upwards and shows the existence of a saddle point (col point) as an extremum (in this case minimum).

This happens at temperatures lower then the critical temperatures of considered binary systems, as has been indicated in Fig.(2.7(b)). Saddle points, also named col points as plait points in general fulfil critical point criteria.

The aim of this chapter is to describe the general principles of experimental methods, which have been used in this work. The chapter is divided into four major sections. The first section (3.1) describes the general aspects of experimental set-ups, to optimize the accuracy of measurements. The second Section (3.2) deals with thedynamic light scattering (DLS)theory and experimental set-up while the third Section (3.3), focused on the broadband ultrasonic (US) theory and experimental setup. A fourth Section (3.4) presents the complementary measurement methods, like shear viscosity, density and calorimetry, which have been used to determine useful thermodynamic parameters.

3.1 General aspects

All technical equipment has been operated in temperature controlled±1 K laboratories.

The specimen cells were provided with channels for circulating thermostat fluid and ad-ditionally placed in thermostatic boxes. This kind of thermostatic shielding allows to control the temperature of the measurement cells to within 0.02 K. The temperature was measured with an error less then 0.01 K using Pt 100 thermometers. In order to avoid mechanical stress during the measurements, the DLS and US cells have been placed on massive granite tables. Both species of cells, the light scattering cells (sample volume 2 ml) as well as ultrasonic cells (samples volume between 2 ml and 200 ml) have been subjected to extremely accurate cleaning procedure before use. The light scattering cells have been treated in an ultrasonic bath cleaner, filled with isopropanol, for several hours before starting a series of measurements. Finally, the cells have been dried in a vacuum oven. In the case of ultrasonic cells the cleaning and preparation procedure is somewhat different. The cells have been first flooded continuously with distilled water for several hours. Afterwards remaining water in the cells has been dissolved by methanol and the cell has been dried with the aid of nitrogen gas for about 30 minutes. The filling pro-cedure of the ultrasonic cells has to be likewise done with care. To avoid air bubbles in the cell the substances have to be filled continuously and slowly from the bottom. The aim is to get the best contact between transducer surface and the investigated substance as well as to avoid air bubbles. Consequently, the speed of cell filling is crucial for the proper operation of the transducers. All measurements have been performed at standard pressure.